General normed spaces are not equipped with an inner product. Nonetheless, there do exist several nonequivalent
extensions of orthogonality from inner product spaces to general normed ones. Arguably, one of the most well-known in this respect is the Birkhoff–James orthogonality, introduced by Birkhoff [1]} and developed by
James [2]}, [3]}, [4]}. It is defined in an arbitrary normed space \((X,\Vert \cdot \Vert )\) 
over the field \(\mathbb {F}\in \lbrace \mathbb {R},\mathbb {C}\rbrace \)  as follows: the vector \(x\in X\)  is
Birkhoff–James orthogonal to \(y\in X\) (shortly: BJ orthogonal; in symbols: \(x\perp y\) ), if
\(\Vert x+\lambda y\Vert \ge \Vert x\Vert ,\quad \forall \lambda \in \mathbb {F}.\) 
